Video Lectures

Mirror symmetry for moduli of flat bundles and non-abelian Hodge theory

April 12, 2017

I will discuss a construction of the homological mirror correspondence on algebraic integrable systems arising as moduli of flat bundles on curves. The focus will be on non-abelian Hodge theory as a tool for implementing hyper Kaehler rotations of...

video lecture

Noncommutative probability for computer scientists

April 11, 2017

Adam Marcus

I will give an introduction to computational techniques in noncommutative probability for people (like myself) that are less interested in the details of the theory and more interested using results in the theory to help understand the behavior of...

video lecture

In pursuit of obfuscation

April 10, 2017

Allison Bishop

This talk will survey some recent advances in research on program obfuscation, an area of theoretical cryptography that has seen unprecedented levels of activity over the last four years. We will cover material starting from the basics, and no prior...

video lecture

Two rigid algebras and a heat kernel

April 07, 2017

Amitai Zernik

Consider the Fukaya A8 algebra $E$ of $RP^{2m}$ in $CP^{2m}$ (with bulk and equivariant deformations, over the Novikov ring). On the one hand, elementary algebraic considerations show that E admis a rigid cyclic minimal model, whose structure...

video lecture

Basic loci of Shimura varieties

April 06, 2017

Xuhua He

In mod-$p$ reductions of modular curves, there is a finite set of supersingular points and its open complement corresponding to ordinary elliptic curves. In the study of mod-$p$ reductions of more general Shimura varieties, there is a "Newton...

video lecture

On Zimmer's conjecture

April 06, 2017

Sebastian Hurtado-Salazar

The group $\mathrm{SL}_n(\mathbb Z)$ (when $n > 2$) is very rigid, for example, Margulis proved all its linear representations come from representations of $\mathrm{SL}_n(\mathbb R)$ and are as simple as one can imagine. Zimmer's conjecture states...

video lecture

Unwinding the amplituhedron

April 05, 2017

Nima Arkani-Hamed

video lecture

Algebra and geometry of the scattering equations

April 03, 2017

Peter Goddard

Four years ago, Cachazo, He and Yuan found a system of algebraic equations, now named the "scattering equations", that effectively encoded the kinematics of massless particles in such a way that the scattering amplitudes, the quantities of physical...

video lecture

A time-space lower bound for a large class of learning problems

April 03, 2017

Ran Raz

We prove a general time-space lower bound that applies for a large class of learning problems and shows that for every problem in that class, any learning algorithm requires either a memory of quadratic size or an exponential number of samples. As a...

video lecture

Rigid holomorphic curves are generically super-rigid

March 31, 2017

Chris Wendl

I will explain the main ideas of a proof that for generic compatible almost complex structures in symplectic manifolds of dimension at least 6, closed embedded J-holomorphic curves of index 0 are always "super-rigid", implying that their multiple...